Question

1. A constant force F = (4.00€ + 5.000) N is applied to a particle that
undergoes a displacement ? = (3.00î - 6.00))m. (a) the work
done by the force, and (b) the component of the force in the
direction of the displacement.​

Answer 1

Answer:

the work done will be = ( 4i + 5j ) . ( 3i - 6j )

= 12 - 30

= - 18 J

here negative work done means that the kinetic energy of the particle will decrease.

the component of a vector along any another vector is calculated by using dot product.

A . B = A B cos( theta)

B cos ( theta) = A . B / A , will be the component of B along Vector A and similarly A cos( theta) will be the component of A along vector B

so in given question

F cos( theta) = F.l / l

= - 18 / √45

second method : u can calculate the unit vector in the direction which u want to calculate the component and take the dot product with the given vector..

unit vector along displacement will be

= ( 3i - 6j) / √45

now take the dot product with given vector that is the force ( here )

= ( 4i +5j ) . ( 3i -6j ) / √45

= - 18 / √ 45

hope this helps..